相关论文: Capturing Hiproofs in HOL Light

A proof tableau of Hoare logic is an annotated program with pre- and post-conditions, which corresponds to an inference tree of Hoare logic. In this paper, we show that a proof tableau for partial correctness can be transformed into an…

For a pointed topological space $X$, we use an inductive construction of a simplicial resolution of $X$ by wedges of spheres to construct a "higher homotopy structure" for $X$ (in terms of chain complexes of spaces). This structure is then…

In this paper two cryptographic methods are introduced. In the first method the presence of a certain size subgroup of persons can be checked for an action to take place. For this we use fragments of Raptor codes delivered to the group…

Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…

Although self-/un-supervised methods have led to rapid progress in visual representation learning, these methods generally treat objects and scenes using the same lens. In this paper, we focus on learning representations for objects and…

We present simple new Hoare logics and refinement calculi for hybrid systems in the style of differential dynamic logic. (Refinement) Kleene algebra with tests is used for reasoning about the program structure and generating verification…

Holographic optical traps use the forces exerted by computer-generated holograms to trap, move and otherwise transform mesoscopically textured materials. This article introduces methods for optimizing holographic optical traps' efficiency…

Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…

Topological data analysis involves the statistical characterization of the shape of data. Persistent homology is a primary tool of topological data analysis, which can be used to analyze topological features and perform statistical…

Typography and layout lead to the hierarchical organisation of text in words, text lines, paragraphs. This inherent structure is a key property of text in any script and language, which has nonetheless been minimally leveraged by existing…

Visual explanation of ``black-box'' models allows researchers in explainable artificial intelligence (XAI) to interpret the model's decisions in a human-understandable manner. In this paper, we propose interpretable class activation mapping…

Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…

Hallucination detection methods for large language models increasingly operate on chain-of-thought reasoning traces, yet it remains unclear whether they evaluate the reasoning itself or merely exploit surface correlates of the final answer.…

Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…

Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…

There are termination proofs that are produced by termination tools for which certifiers are not powerful enough. However, a similar situation also occurs in the other direction. We have formalized termination techniques in a more general…

We present a tool for verification of hybrid systems expressed in the sequential fragment of HCSP (Hybrid Communicating Sequential Processes). The tool permits annotating HCSP programs with pre- and postconditions, invariants, and proof…

This work presents a formalized proof of modal completeness for G\"odel-L\"ob provability logic (GL) in the HOL Light theorem prover. We describe the code we developed, and discuss some details of our implementation, focusing on our choices…

Transcribing content from structural images, e.g., writing notes from music scores, is a challenging task as not only the content objects should be recognized, but the internal structure should also be preserved. Existing image recognition…

With the popularity of deep neural networks (DNNs), model interpretability is becoming a critical concern. Many approaches have been developed to tackle the problem through post-hoc analysis, such as explaining how predictions are made or…